# Kernel Bounds for Structural Parameterizations of Pathwidth

@article{Bodlaender2012KernelBF, title={Kernel Bounds for Structural Parameterizations of Pathwidth}, author={Hans L. Bodlaender and Bart M. P. Jansen and Stefan Kratsch}, journal={ArXiv}, year={2012}, volume={abs/1207.4900} }

Assuming the AND-distillation conjecture, the Pathwidth problem of determining whether a given graph G has pathwidth at most k admits no polynomial kernelization with respect to k. The present work studies the existence of polynomial kernels for Pathwidth with respect to other, structural, parameters.
Our main result is that, unless NP ⊆ coNP/poly, Pathwidth admits no polynomial kernelization even when parameterized by the vertex deletion distance to a clique, by giving a cross-composition…

## 17 Citations

### Preprocessing for Treewidth: A Combinatorial Analysis through Kernelization

- Computer ScienceSIAM J. Discret. Math.
- 2011

This work seeks to prove rigorous performance guarantees for such preprocessing rules---known rules as well as more recent ones---by studying them in the framework of kernelization from parameterized complexity.

### FPT is characterized by useful obstruction sets: Connecting algorithms, kernels, and quasi-orders

- Computer Science, MathematicsTOCT
- 2014

This work shows how exponential-size minor-minimal obstructions for pathwidth k form the crucial ingredient in a novel or-cross-compositions for k-Pathwidth, complementing the trivial and-composition that is known for this problem.

### Preprocessing subgraph and minor problems: When does a small vertex cover help?

- Mathematics, Computer ScienceJ. Comput. Syst. Sci.
- 2012

These characterizations not only give generic explanations for the existence of many known polynomial kernels for problems like q-Coloring, Odd Cycle Transversal, Chordal Deletion, @h-Transversal or Long Path, parameterized by the size of a vertex cover, but also imply new polynometric kernels for Problems like F-Minor-Free Deletions.

### Kernelization Using Structural Parameters on Sparse Graph Classes

- Mathematics, Computer ScienceESA
- 2013

This paper shows that graph problems that have finite integer index (FII) admit linear kernels on hereditary graphs of bounded expansion when parameterized by the size of a modulator to constant-treedepth graphs, and proves meta-theorems for these three graph classes.

### The Power of Data Reduction : Kernels for Fundamental Graph Problems

- Computer Science, Mathematics
- 2013

The concept of kernelization, developed within the field of parameterized complexity theory, is used to give a mathematical analysis of the power of data reduction for dealing with fundamental NP-hard graph problems and it is proved that Treewidth and Pathwidth do not admit polynomial kernels parameterized by the vertex-deletion distance to a clique, unless thePolynomial hierarchy collapses.

### On Cutwidth Parameterized by Vertex Cover

- Mathematics, Computer ScienceAlgorithmica
- 2012

This work gives the first non-trivial exact exponential time algorithm for Cutwidth on a graph class where the problem remains NP-complete and shows that Cutwidth parameterized by the size of the minimum vertex cover of the input graph does not admit a polynomial kernel unless NP⊆coNP/poly.

### Experimental Evaluation of a Branch-and-Bound Algorithm for Computing Pathwidth and Directed Pathwidth

- Computer ScienceACM J. Exp. Algorithmics
- 2016

A branch-and-bound algorithm that computes the exact pathwidth of graphs and a corresponding path decomposition and achieves good performance when used as a heuristic (i.e., when returning best result found within bounded time limit).

### TREEWIDTH and PATHWIDTH parameterized by vertex cover

- Mathematics, Computer ScienceArXiv
- 2013

It is shown that the PATHWIDTH and TREEWIDTH can be computed in O*(3^k) time, which complements recent polynomial kernel results for TREEWidTH and PATHWidTH parameterized by the Vertex Cover.

### Treewidth and Pathwidth parameterized by the vertex cover number

- MathematicsDiscret. Appl. Math.
- 2013

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